"Language reflects reality imperfectly, but it's by far the best medium we have to express what is, as well as what was and what might yet be. Simply put, we are logocentric creatures. Style matters because it shows our interlocutors that we take our—and their—verbal expressions seriously. And for many of us, an appreciation of words is ultimately an appreciation of *logos*, of the Word."
— Joshua T. Katz
Language is fascinating. It is a weird communication interface because each of us has our own internal vocabulary. Words are useful because they mean similar things to many people, but there is no way to ensure that words have identical meaning between people.
This is really powerful because it allows language to act as a communication and translation layer between completely unique environments (heads) the only sure way to communicate is through dialog in order to come to a shared understanding.
This makes bandwidth low, but I think that is a feature. If bandwidth were high I might not be able to distinguish between my own thoughts and yours. I wouldn't know which ideas need closer verification. The slow twisted process of language is what builds our sense of self.
It also allows different minds to treat ideas differently. This is a defense against general exploits and a source of new ideas.
Do you think that it is possible to have thoughts independent of language?
Yes. Though maybe not symbolic thoughts. I plainly don't use language to plan complex physical motions in real time. Stuff like deciding a path to take through a bunch of trees. I also don't use language to do mental rotations etc. but I have never succeeded in thinking about anything abstract with language. I have heard of people who claim they don't but I am not sure I believe them.
There's definitely image-based thinking and word-based thinking. Maybe we could add symbol-based thinking underneath both. Words and images are both symbols.
That is distinct from the sort of embodied thinking you described, like planning a path to walk or playing an instrument.
I would argue that abstract concepts often come into the mind *before* we have the language to describe them. The symbols allow us to grasp the concepts concretely.
Having something "on the tip of your tongue" would seem to be an instance of an abstract concept preceding the language used to grasp it.
That is a great point. But having something on the tip of your tongue is also one of the most frustrating exercises in thinking. It feels incomplete. I have often wondered, however, if we could develop an internal symbol set that was not constrained by time to speed up thinking. By "constrained by time" I mean that words, being serialized sound pressure levels necessarily take time to utter and thus to think.
Since viseospacial reasoning can happen much faster it gives me hope that it is somewhat possible.
We need a token set with no pronunciation and a method of translation. Would be cool if it could be transmitted without translation though. Just write out the tokens for other people to read in. Maybe someone deaf from birth would do a better job of developing it.
Picture thinkers seem to have that, so some degree. An image that represents a concept is faster to summon than a sentence that describes the same concept.
That said, I'm not too concerned about speed; thought already moves much faster than words, even if it takes non-zero time.
The fastest thought would be pre-symbolic, almost by definition. Spelling out concepts will necessarily take time.
I care about speed because I'd rather hear words at the end of a "thought much and said little" process than a stream-of-concious word dump.
Also I like math and logical reasoning. Language is only sorta useful for that. We have to come up with special definitions of words for logical contexts. Programming is an excellent case. By if we mean "if and only if" and or is not exclusive OR. If the symbols, oft times, WERE the conclusion I wouldn't have to hold so much in my head at once.
You'll have to forgive me, I want this to be able to solve the twin prime conjecture, but I run into a hard limit on the complexity that I can reason about at once. I wonder if I could offload some of the work onto a symbolic system that maintains part of the state for me.
Can you explain the twin prime conjecture? I'm not super familiar with it.
There are infinite pairs of primes such that P_n+1 - P_n = 2. Examples are (3,5),(5,7),(11,13),(17,19) etc..
The best I can do is prove that there are infinitely pairs coprime to any list of primes. Basically you can't give me any list of primes up to but not including infinity for which I couldn't find a pair of number separated by two neither of which have any factors in your list.
So the question is how to generalize from lists of coprimes to *all* the primes, right?
Kind of. You don't have to generalize to all the primes if you can show that at least one of the co-prime pairs is "small." small being less than the square of the largest prime in your list.. as long as your list is all the primes up to that prime.
If the co-prime twins are evenly distributed then this shouldn't be a problem there will be an ever increasing number of twin prime candidates less than the square as the list gets longer. But the best I can do there is show that there will be PI[(p_n-1)/(p_n-2)] / 2 less than PI[pn-1] / 2
PI being the product of all the terms. Unfortunately the numbers get so massive compared to p_n^2 that I can't really say anything conclusive even though there should be plenty. I need headspace to think about larger patterns of gaps between gaps of primes. I.e. if the twin primes are far enough apart then they need to spread out enough to have some less than p_n^2.
